Mathematics of XMCQDPT

The Complete Active Space Self-Consistent Field (CASSCF) method provides an excellent description of static electron correlation by explicitly including all important electronic configurations within a chosen active space.

However, electrons occupying inactive and virtual orbitals still interact with the active electrons. These interactions, known as dynamic electron correlation, are not included in the CASSCF energy.

The Extended Multi-Configuration Quasi-Degenerate Perturbation Theory (XMCQDPT) method introduces these missing correlation effects through second-order perturbation theory while preserving the multiconfigurational character of the CASSCF wavefunction.

Unlike CASSCF, XMCQDPT is not variational. Instead, it treats the optimized CASSCF wavefunction as a reference and computes perturbative corrections arising from excitations outside the active space.

This section develops only the mathematical concepts that are added beyond CASSCF.

Topics Covered

1. Zeroth-Order Hamiltonian
2. Perturbation Expansion
3. Effective Hamiltonian
4. Intermediate-State Formalism
5. Second-Order Energy Corrections
6. Final XMCQDPT Energies
7. Advantages over CASSCF